Rees algebras of sparse determinantal ideals

Celikbas, Ela; Dufresne, Emilie; Fouli, Louiza; Gorla, Elisa; Lin, Kuei-Nuan; Polini, Claudia; Swanson, Irena

doi:10.1090/tran/9101

Rees algebras of sparse determinantal ideals
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by Ela Celikbas, Emilie Dufresne, Louiza Fouli, Elisa Gorla, Kuei-Nuan Lin, Claudia Polini and Irena Swanson;

Trans. Amer. Math. Soc. 377 (2024), 2317-2333

DOI: https://doi.org/10.1090/tran/9101

Published electronically: February 14, 2024

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Abstract:

We determine the defining equations of the Rees algebra and of the special fiber ring of the ideal of maximal minors of a $2\times n$ sparse matrix. We prove that their initial algebras are ladder determinantal rings. This allows us to show that the Rees algebra and the special fiber ring are Cohen-Macaulay domains, they are Koszul, they have rational singularities in characteristic zero and are F-rational in positive characteristic.

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